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On incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion and purely spherical elastic response
Type of publication: Article
Citation:
Publication status: Published
Journal: SIAM J. Math. Anal.
Volume: 53
Number: 4
Year: 2021
Pages: 3985--4030
DOI: 10.1137/20M1384452
Abstract: We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary condition for the velocity and a homogeneous Neumann boundary condition for the extra stress tensor. In the introductory section we develop the thermodynamic foundations of the proposed model, and we document the role of thermodynamics in obtaining critical structural relations between the quantities of interest. These structural relations are then exploited in the mathematical analysis of the governing equations. In particular, the definition of weak solution is motivated by the thermodynamic basis of the model. The extra stress tensor describing the elastic response of the fluid is in our case purely spherical, which is a simplification from the physical point of view. The model nevertheless exhibits features that require novel mathematical ideas in order to deal with the technically complex structure of the associated internal energy and the more complicated forms of the corresponding entropy and energy fluxes. The paper provides the first rigorous proof of the existence of large-data global-in-time weak solutions to the governing equations for \emph{coupled thermo-mechanical processes} in viscoelastic rate-type fluids.
Preprint project: NCMM
Preprint year: 2020
Preprint number: 06
Preprint ID: NCMM/2020/06
Keywords: global-in-time existence, Incompressible fluid, non-Newtonian fluid, stress-diffusion, viscoelastic fluid, weak solution, \\ temperature-dependent material moduli
Authors Bulíček, Miroslav
Málek, Josef
Průša, Vít
Süli, Endre
Added by: [MB]
Total mark: 0
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